Appendix 4.1

Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Appendix 4.1

Alternate Proofs of Selected HO Theorems

Copyright © 2010 Pearson Addison-Wesley. All rights reserved.4.1-2

Production Isoquant

• An isoquant shows the various combinations of labor and capital required to produce a fixed quantity of a product.

• The curvature of an isoquant indicates the ease of subsitutability between the two inputs, holding output constant.

• A straight line isoquant indicates that the inputs are perfect substitutes; right angles indicate that inputs are not substitutable.


FIGURE A4.1 Isoquant Map for the S Industry


Heckscher-Ohlin Theorem (Price Definition)• If country A (B) is relatively abundant in K

(L) and if good S (T) is relatively K (L)– intensive in its production, then country A (B) should have a comparative advantage in the production of good S (T).


Proof of HO Theorem

• See Figure A4.2• There are two isoquants, each representing the

production of one unit of good S (T).• The S isoquant is closer to the K-axis indicating that

S is more K-intensive. • The least costly input combination for producing a

desired output level occurs at the tangency of an isocost line (such as GH) and an isoquant (such as point R for good S).


FIGURE A4.2 Proof of the HO Theorem (Price Definition)


HO Theorem Proof (cont.)

• If isocost line GH is tangent to both S and T isoquants (at points R and Q), then the cost of producing each product must be identical.

• The slope of isocost line GH is equal to country A’s autarky wage/rent ratio; GH cannot apply to country B.

• Since B is more labor abundant than A, its wage/rent ratio is lower than A’s.

• The isocost line to produce good S in country B is higher than the isocost line to produce T; thus, B has a comparative advantage in good T.


Proof of the Rybczynski Theorem• Refer to Figure A4.3• Given isoquants representing $1 each of

goods S and T and an isocost line tangent to both, the tangency points F and D represent optimal input combinations.

• The slopes of the rays from the origin passing through F and D indicate the optimal capital/labor use ratios.


Rybczynski Theorem (cont.)

• Given factor endowments represented by point E, draw a parallelogram connecting E to the two rays from the origin. Adding the factor combination OG (OH) to point H (G) will result in total endowment level E.

• When the country’s labor rises (capital and prices constant), the endowment level moves from E to E’. As a result, the output of S falls to G’ while T rises to H’.


FIGURE A4.3 Proof of the Rybczynski Theorem


Proof of Stolper-Samuelson Theorem• Refer to Figure A4.4• The initial optimal input combinations are indicated

by the tangency points F and D.• If the price of T rises, then a $1 worth of this good is

now on a lower isoquant T’. A new isocost line is tangent to the isoquants S and T’.

• A comparison of the isocost lines shows that wages have risen while rents have fallen. As a result, labor (capitalists) can purchase more (less) of both goods.


FIGURE A4.4 Proof of the Stolper–Samuelson Theorem


FIGURE A4.5 Equilibrium in the Specific Factors Model


Specific Factors (Ricardo-Viner) Model

• Same assumptions as HO Model except capital is immobile between industries

• Refer to Figure A4.5• The horizontal axis measures labor input in

A, with labor units in S (T) industry measured from point 0S (0T). The vertical axes measure wage rate in A.

• The VMPS curve shows the S industry’s demand for labor; the industry will hire labor until W =PS x MPLS. Likewise for VMPT curve.


Equilibrium in Specific Factors Model

• Labor market equilibrium occurs at the intersection of the VMPS and VMPT curves.

• 0SD workers are employed in the S industry and D0T workers in the T industry.

• Wage rate paid to workers in both sectors is W0.


Effects of a Rise in Price of Good S

• Country A has a comparative advantage in S. When trade opens up, the price of S rises.

• Demand for labor will increase in industry S; employment in S rises while employment in the T sector falls. Wages also increase.

• Capital owners in industry S are better off as their rental payments rise.


FIGURE A4.6 Effects of an Increase in PS

Appendix 4.1

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